Key Features of Functions

Front

What is the initial height of a projectile in a function?

Back

The initial height of a projectile is the value of the function at time t=0, which represents the starting point of the projectile's motion.

Front

On what interval is a function decreasing?

Back

A function is decreasing on an interval where the output values (y-values) are getting smaller as the input values (x-values) increase.

Front

What is a relative minimum in a graph?

Back

A relative minimum is a point on the graph where the function value is lower than the values of the function at nearby points.

Front

How can you identify a y-intercept on a graph?

Back

A y-intercept is identified as the point where the graph crosses the y-axis, which occurs when the x-coordinate is 0.

Front

What does it mean if a function has no maximum?

Back

If a function has no maximum, it means that the function continues to increase indefinitely without reaching a highest point.

Front

What are the maximum and minimum points of a function?

Back

Maximum points are the highest points on a graph, while minimum points are the lowest points. They can be found by analyzing the function's critical points.

Front

What is the significance of the vertex in a quadratic function?

Back

The vertex of a quadratic function represents the maximum or minimum point of the parabola, depending on its orientation.

Front

How do you determine the intervals of increase and decrease for a function?

Back

To determine intervals of increase and decrease, analyze the first derivative of the function; where the derivative is positive, the function is increasing, and where it is negative, the function is decreasing.

Front

What is the role of the discriminant in quadratic functions?

Back

The discriminant (b² - 4ac) determines the nature of the roots of a quadratic function: if it's positive, there are two real roots; if zero, one real root; if negative, no real roots.

Front

What is the difference between absolute and relative extrema?

Back

Absolute extrema are the highest or lowest points over the entire domain of the function, while relative extrema are the highest or lowest points in a specific interval.